On a delayed invasive species model with harvesting

Sándor Kovács; Szilvia György

doi:10.3934/dcdsb.2024005

Article Contents

2024, Volume 29, Issue 8: 3297-3325. Doi: 10.3934/dcdsb.2024005

This issue Previous Article Stress formulation and duality approach in periodic homogenization Next Article Sobolev-Lorentz spaces with an application to the inhomogeneous biharmonic NLS equation

On a delayed invasive species model with harvesting

Sándor Kovács^, and
Szilvia György

Department of Numerical Analysis, ELTE Eötvös Loránd University, Budapest, Pázmány Péter sétány 1/C, Hungary

^*Corresponding author: Sándor Kovács
^*Corresponding author: Sándor Kovács

Received: August 2020

Revised: August 2023

Early access: January 2024

Published: August 2024

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Abstract

In this paper a mathematical model will be studied that describes the connections between three species: people, trees and rats. This model, which is based on a three-dimensional system of ordinary differential equations, has been motivated by attempts to explain the ecological disaster of Easter Island. The system has four equilibria from which three ones are on the boundary of the positive octant of the phase space and – under appropriate conditions – there is a unique interior equilibrium. We incorporate discrete delay into the system in order to have a more realistic model. This delay takes into account that time is needed for the seeds to become a full-grown tree. The stability of the equilibria with delay and the possibility of an oscillatory behaviour are examined.

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Mathematics Subject Classification: Primary: 92B05, 93D05; Secondary: 34C23, 34D20, 37N25.

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Figure 1. Time evolution of system (1) before Hopf bifurcation

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Figure 2. Time evolution of system (2) after Hopf bifurcation

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